As an instructor, it is my job to determine who is ready, and when - not the students. This goes for adults as well as kids. If I allow a student to test who is not ready, that is my fault. On the other hand, if I allow a student to test who is capable of passing, and the student performs badly, that may or may not be my fault. Lack of effort on the student's part is the student's fault; something going on in the student's life that affects the student's ability to pass... it depends. One of my students tested for BB and had some problems - but it was because her father had just completed chemo for prostate cancer; watching his then 17 year-old test was the first time he'd been out of the house since he finished, and they weren't sure of his prognosis at the time (he's fine now, and it's been 4 years) - she had an excuse to be a little off, and appropriate allowances were made. Another student I know celebrated too much the night before testing, showed up horribly hung-over, and flunked... and that was his own fault.
I would not hold an instructor responsible for a child's failure outside the dojang... inside, yes. Students should either learn to behave appropriately for their rank and MA, or they should not be allowed in the dojang. I have had students who were not allowed to re-enroll (rare), and students who chose not to re-enroll because they didn't want to work hard enough to meet my expectations (rare, but less so than the first one). As an instructor, it is my responsibility to provide an appropriate environment for all students, and to help them achieve success - and if they don't, it is my fault. I have had plenty of parents ask me how to get their kids to behave for them at home the way they do for me at the dojang; the difference is, I'm not their parent, the dojang is not their home, and the circumstances are different. Students behave, or their are consequences. In very extreme circumstances, the consequence is losing the privilege of attending class - generally when the safety of other students is impacted.
See, I have a problem with the dichotomy here - if the child does well, it's because of the instructor, but if the child does poorly, it's everyone else. I don't think you can have it both ways.
Sort of; the kid was spoiled rotten, and had no idea how to handle anything other than being told how wonderful he was; other parents whose kids went to the same elementary school said mom had the same problems with his teacher each year.